Partition functions, conformational changes

Hesselink23) attempted to calculate adsorption isotherms for flexible polyelectrolytes. He assumed that, when adsorbed on a surface, a flexible polyelectrolyte takes a conformation consisting of one train and one tail. The theoretical treatment of Hoeve et al.4I) (cf. B.3.1) for non-ionic polymers was extended by taking into account the change in electrical free energy that occurs when the polyelectrolyte is brought from the solution onto the interface. The partition function Q for a system of N polyelectrolytes each consisting of n units, in which Na polyions are adsorbed on the surface of area S and Nf(Nf = N - N ) polyions remain in the bulk solution of volume V, is then represented by... 

Consider a solute s with internal rotational degrees of freedom. We assume that the vibrational, electronic, and nuclear partition functions are separable and independent of the configuration of the molecules in the system. We define the pseudo-chemical potential of a molecule having a fixed conformation Ps as the change in the Helmholtz energy for the process of introducing s into the... 

The conformer distribution estimated above leads to the configurational partition function Zn for the nematic state. Since the partition function Zj for the isotropic state is available from the conventional RIS calculation, the conformational entropy change 5 at the NI interphase may be obtained as... 

ZfN) (not to be confused with Z, the number of entanglements on a polymer) is the partition function of a LP with N beads and is indicative of the total number of conformations that it may adopt. As shown in Sections 7.3 and 7.4, static properties of LPs are unaffected by the composition of the CLB hence is assumed to be independent of ( )c. The partition function Zf N) does not enter into calculations explicitly, beyond an additive constant, which cancels out when we calculate MN, c) is the probability with which an LP adopts a conformation in which its ends overlap. The second equality in Equation (7.25) offers a more tractable computational route to calculate P Rc)-Computation of F Rc) thus requires knowledge of (a) X N, ( )c), the probability with which an LP adopts a conformation indistinguishable from lhat of a CP, which occurs when its ends essentially overlap, and (b) P Rc), the probability density function of CPs characterized using the size Rc as the macrostate variable. These quantities are expected to change with the composition of the CLB. 

Hydration of a neutral polymer can roughly be classified into two categories direct hydrogen bonds (referred to as H-bonds) between a polymer chain and water molecules (p-w), and the hydrophobic hydration of water molecules surrounding a hydrophobic group on a chain in a cage structure by water-water (w-w) H-bonds. In this section, we extend the combinatorial method for the partition function presented in the previous section to suit for the problem of solvent adsorption, and study polymer conformation change in aqueous solutions due to the direct p-w H-bonds. 

The change in the conformational entropy of a chain on fusion, at constant volume, can be evaluated from the partition function of the disordered chain, if it is assumed that there are no contributions from the ordered structure. Thus, the conformational entropy on fusion is identified with the entropy of the isolated chain in the pure melt. This entropy can be written as... 

How does the population of collapsed conformations change as the temperature is changed We focus here on the two macrostates, open and compact, rather than on the individual microstates, so the partition function for this... 

Suppose a chain has N monomer units. Assume that the state (H or C) of each monomer j = 1,2,3,...,N in the chain is independent of the state of every other monomer. Let qc be the partition function for each C unit. Let qn be the partition function for each H unit. Because any conformational change can always be expressed as the ratio of these quantities, you are free to choose qc = 1, which is equivalent to setting the free energy of a coil unit equal to zero. Let qn = exp(- s), where f < 0 represents the energy of forming a helical unit relative to a coil unit, and = l/kT. The ratio... 

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